Question

Let $n>2$ be an integer. Suppose that there are $n$ Metro stations in a city located along circular path. Each pair of stations is connected by a stright track only. Further, each pair of nearest stations is connected by blue line, whereas all remaining pairs of stations are connected by red line. If the number of red lines is $99$ times the number of blue lines, then the value of $n$ is:

• A. $201$
• B. $199$
• C. $101$
• D. $200$

Answer 1

The correct option is A $201$


Red line $=99$ blue line
$\Rightarrow n_{C_2}-n=99n$
$\Rightarrow \frac{n(n-1)}{2}=100n$
$\Rightarrow n-1=200$
$\Rightarrow n=201$